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    <title>householder</title>
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    <center>Scilab Function</center>
    <div align="right">Last update : April 1993</div>
    <p>
      <b>householder</b> -  Householder orthogonal reflexion matrix</p>
    <h3>
      <font color="blue">Calling Sequence</font>
    </h3>
    <dl>
      <dd>
        <tt>u=householder(v [,w])  </tt>
      </dd>
    </dl>
    <h3>
      <font color="blue">Parameters</font>
    </h3>
    <ul>
      <li>
        <tt>
          <b>v</b>
        </tt>: real or complex column vector</li>
      <li>
        <tt>
          <b>w</b>
        </tt>: real or complex column vector with same size as <tt>
          <b>v</b>
        </tt>. Default value is <tt>
          <b>eye(v)</b>
        </tt>
      </li>
      <li>
        <tt>
          <b>u</b>
        </tt>: real or complex column vector</li>
    </ul>
    <h3>
      <font color="blue">Description</font>
    </h3>
    <p>
    given 2 column vectors <tt>
        <b>v</b>
      </tt>, <tt>
        <b> w</b>
      </tt> of same size, <tt>
        <b>householder(v,w)</b>
      </tt> returns a unitary 
    column vector <tt>
        <b>u</b>
      </tt>, such that <tt>
        <b> (eye()-2*u*u')*v</b>
      </tt> is proportional to <tt>
        <b>w</b>
      </tt>.
    <tt>
        <b>(eye()-2*u*u')</b>
      </tt> is the orthogonal Householder reflexion matrix .</p>
    <p>
      <tt>
        <b>w</b>
      </tt> default value is <tt>
        <b> eye(v)</b>
      </tt>. In this case vector <tt>
        <b> (eye()-2*u*u')*v</b>
      </tt> is the 
    vector  <tt>
        <b> eye(v)*norm(v)</b>
      </tt>.</p>
    <h3>
      <font color="blue">See Also</font>
    </h3>
    <p>
      <a href="qr.htm">
        <tt>
          <b>qr</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="givens.htm">
        <tt>
          <b>givens</b>
        </tt>
      </a>,&nbsp;&nbsp;</p>
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